GCSE Maths · Higher · Chapter 16: Counting, accuracy, powers and surds · Lesson 4

Limits of accuracy

Grades 5–8About 50 minutesCalculator allowed35 marks

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NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
Round $8319.2$ to 2 significant figures.
[1 mark]
Answer
A2
Last lesson
Simplify $32$ .
[1 mark]
Answer
A3
From chapter 11
A cuboid is 2 cm by 3 cm by 6 cm. Find the length of its longest diagonal.
[1 mark]
Answer
A4
From chapter 11
In a right-angled triangle the opposite and adjacent sides are both 3 cm. Find the angle.
[1 mark]
Answer

Grades 5–7

Your teacher works through each example with you. Then try the one beside it.

Example 1

A length is 6.4 cm to 1 decimal place. Write its error interval, $l$ cm.

Hint Go half of 0.1 either side. The upper bound is not included.

B1
A mass is 2.38 kg to 2 decimal places. Write its error interval, $m$ kg.
[2 marks]
Answer $\dots\dots \leq m < \dots\dots$

Example 2

Lengths of 8.3 cm and 5.6 cm are each to 1 decimal place. Work out their smallest possible difference.

Hint Take the smallest first length and the largest second length.

B2
A plank 46 cm long has a 17 cm piece cut off. Both are to the nearest cm. Work out the largest possible length left.
[3 marks]
Answer

Grades 6–7

C1
A school has 860 pupils, to the nearest 10. Write down the largest possible number of pupils.
[1 mark]
Answer
C2
A number $x$ is 3500, correct to 2 significant figures. Write down the error interval for $x$ .
[2 marks]
Answer $\dots\dots \leq x < \dots\dots$

C3
Ana truncates a number $y$ to 1 decimal place. The result is $7.2$ . Write down the error interval for $y$ .
[2 marks]
Answer $\dots\dots \leq y < \dots\dots$
C4
A bag of sand has a mass of 25 kg, to the nearest kg. Work out the lower bound of the total mass of 4 bags.
[2 marks]
Answer
C5
A square has sides of 7 cm, to the nearest cm. Work out the lower bound of its area.
[2 marks]
Not drawn accurately
Answer
C6
A rectangle is 12 cm by 5 cm, each to the nearest cm. Work out the upper bound of its perimeter.
[2 marks]
Not drawn accurately
Answer

Grades 7–8

D1
Ravi says, "A rope is 4.7 m long, correct to 1 decimal place, so it could be 4.75 m long."
Explain why Ravi is wrong.
[2 marks]

D2
A coach travels 120 km, correct to the nearest 10 km. The journey takes 3 hours, correct to the nearest hour.
(a)
Write down the upper bound of the distance and the lower bound of the time.
[2 marks]
Answer $\dots\dots$ km and $\dots\dots$ hours
(b)
Work out the upper bound of the average speed.
[2 marks]
Answer
(c)
The driver says, "The average speed was certainly more than 30 km/h." Is the driver right? Show how you decide.
[2 marks]
Total for D2: 6 marks
D3
A rectangle has an area of 54 cm², correct to 2 significant figures. Its length is 9.2 cm, correct to 1 decimal place. Work out the width $w$ of the rectangle to a suitable degree of accuracy. You must show your working and give a reason for your answer.
[4 marks]
Not drawn accurately
Answer

Grade 9 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can write an error interval for a rounded or a truncated value.
I can choose the right bounds for a sum or a difference.
I can choose the right bounds for a product or a quotient.

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